【摘要】
In this talk, I will go through some recent developments over the optimal degeneration of Fano varieties. Given a Fano variety X, there exists a two-step degeneration procedure to produce a weighted K-polystable variety X’. The degeneration is optimal in the sense that it is the minimizer of an algebraic invariant. In addition, there exists a (unique) singular Kähler Ricci soliton metric on X’. The degeneration procedure is essential an algebraic analogue of the Hamilton-Tian conjecture for the Kähler Ricci flow.
